The poll of likely Republican caucusgoers, released Tuesday, has Herman Cain at 20 percent, Ron Paul at 19 percent, Mitt Romney at 18 percent, and Newt Gingrich at 17 percent – all within the poll's 4-point margin of error.

Mr. Romney has been downplaying his chances – and has long been considered an underdog in Iowa – but now seems to be making a real run for the state. And he's been remarkably steady in the polls there, even as the other candidates all go through their moments in the sun.

Given the dynamics of the Iowa caucuses, including their tendency to attract more committed and conservative members of the Republican Party, an Iowa win for Romney would be huge.

Of course, Iowa isn't always the best predictor of who will eventually get the nomination. In 2008, Mike Huckabee won. Romney came in second (after expending a huge amount of money and manpower in the state), Fred Thompson was third, and eventual nominee John McCain was fourth, with 13 percent of the vote.

But a win that early is a strong start for any candidate and can give momentum to a campaign that carries over to other races. President Obama's big 2008 win in the Democratic caucuses was the first sign that he was a force to be reckoned with, and John Kerry's unexpected win in 2004 gave a boost to his campaign that helped propel him to the nomination.

As recently as this week, Romney has reportedly been telling supporters that he expects to lose Iowa, but then win in New Hampshire and – even more importantly – in Florida a couple weeks later.

It's a plausible scenario. But if Romney can actually pull out a win in Iowa (and with the anti-Romney contingent seemingly so split, it's a very real possibility), it would be huge for the former Massachusetts governor, and would seem to make a Romney nomination almost inevitable.

That's the big reason Romney has stayed somewhat active in the state – including a handful of campaign visits and robocalls attacking Rick Perry – but he also has some reason to be wary.

In that same Bloomberg poll, 58 percent of the respondents said they would rule out voting for any candidate who had previously supported a mandate to buy health insurance. That's more than the number ruling out a candidate for any other reason asked in the poll, including a candidate who had worked for the Obama administration (40 percent), who had supported the pro-immigration DREAM Act (42 percent), or who had been married three times and had extramarital affairs (48 percent). Some 33 percent also said they would rule out supporting a candidate who had changed position on abortion – another area where Romney is vulnerable.

On the other hand, Romney has a lot of voters he can still hope to persuade. Fewer than 30 percent told Bloomberg that their mind was made up, and 60 percent said they could be persuaded to support another candidate as their first choice.